Showing papers on "Multiresolution analysis published in 2021"

Laplacian Pyramid Dense Network for Hyperspectral Pansharpening

Abstract: Hyperspectral (HS) pansharpening aims to create a pansharpened image that integrates the spatial details of the panchromatic (PAN) image and the spectral content of the HS image. In this article, we present a deep convolutional network within the mature Gaussian-Laplacian pyramid for pansharpening (LPPNet). The overall structure of LPPNet is a cascade of the Laplacian pyramid dense network with a similar structure at each pyramid level. Following the general idea of multiresolution analysis (MRA), the subband residuals of the desired HS images are extracted from the PAN image and injected into the upsampled HS image to reconstruct the high-resolution HS images level by level. Applying the mature Laplace pyramid decomposition technique to the convolution neural network (CNN) can simplify the pansharpening problem into several pyramid-level learning problems so that the pansharpening problem can be solved with a shallow CNN with fewer parameters. Specifically, the Laplacian pyramid technology is used to decompose the image into different levels that can differentiate large- and small-scale details, and each level is handled by a spatial subnetwork in a divide-and-conquer way to make the network more efficient. Experimental results show that the proposed LPPNet method performs favorably against some state-of-the-art pansharpening methods in terms of objective indexes and subjective visual appearance.

Concrete Cracks Detection and Monitoring Using Deep Learning-Based Multiresolution Analysis

Abstract: In this paper, we propose a new methodology for crack detection and monitoring in concrete structures. This approach is based on a multiresolution analysis of a sample or a specimen of concrete material subjected to several types of solicitation. The image obtained by ultrasonic investigation and processed by a customized wavelet is analyzed at various scales in order to detect internal cracks and crack initiation. The ultimate objective of this work is to propose an automatic crack type identification scheme based on convolutional neural networks (CNN). In this context, crack propagation can be monitored without access to the concrete surface and the goal is to detect cracks before they are visible. This is achieved through the combination of two major data analysis tools which are wavelets and deep learning. This original procedure is shown to yield a high accuracy close to 90%. In order to evaluate the performance of the proposed CNN architectures, we also used an open access database, SDNET2018, for the automatic detection of external cracks.

Combining Deep Learning and Multiresolution Analysis for Stock Market Forecasting

Abstract: Due to its complexity, financial time-series forecasting is regarded as one of the most challenging problems. During the past two decades, nonlinear modeling techniques, such as artificial neural networks, were commonly employed to solve a variety of time-series problems. Recently, however, deep neural network has been found to be more efficient than those in many application domains. In this article, we propose a model based on deep neural networks that improves the forecasting of stock prices. We investigate the impact of combining deep learning techniques with multiresolution analysis to improve the forecasting accuracy. Our proposed model is based on an empirical wavelet transform which is shown to outperform traditional stationary wavelet transform in capturing price fluctuations at different time scales. The proposed model is demonstrated to be substantially more effective than other models when evaluated on the S&P500 stock index and Mackey-Glass time series.

Fault Protection in Microgrid Using Wavelet Multiresolution Analysis and Data Mining

Abstract: The protection problems in microgrid effect the reliability of the power system caused due to high distributed generator penetrations. Therefore, fault protection in microgrid is extremely important and needs to be resolved to enhance the robustness of the power system. This manuscript proposes a combined signal processing and data mining-based approach for microgrid fault protection. In this study, first the multiresolution decomposition of wavelet transform is employed to preprocess the voltage and current signals to compute the total harmonic distortion of the voltage and current. Then, the statistical indices of standard deviation, mean, and median of the total harmonic distortion and the negative sequence components of active and reactive power are used to collect the input data. After that, all the available data is provided to the random forest-based classifier to evaluate the efficiency of the proposed scheme in terms of the detection, identification, and classification of faults. This study used different aspects for data collection by simulating various fault and no-fault cases for both looped and radial configurations under grid-connected and islanded modes of operation. The simulations were performed on a standard medium voltage microgrid using MATLAB/SIMULINK, whereas the analysis for testing and training of the random forest were conducted in Python. It is recognized that the proposed method performed better than support vector machines and decision tree that are reported in the literature. The results further demonstrate that the proposed method can also detect simultaneous faults, and it is also effective against measurement noise.

Theory and Design of Joint Time-Vertex Nonsubsampled Filter Banks

Abstract: Graph signal processing (GSP) is a field that deals with data residing on irregular domains, i.e. graph signals. In this field, the graph filter bank is one of the most important developments, owing to its ability to provide multiresolution analysis of graph signals. However, most of the current research on graph filter bank focuses on static graph signals. The research does not exploit the temporal correlations of time-varying signals in real-world applications, such as in wireless sensor networks. In this paper, the theory and design of joint time-vertex nonsubsampled filter bank are developed, using a generalized product graph framework. Several methods are proposed to design the filter bank with perfect reconstruction, while still achieving filters with good spectral characteristics. A notable feature of the designed filter bank is that it can be completely realized in a distributed manner. The subband filters are either of polynomial type or defined implicitly via iterative equations. In either case, implementing the subband filters requires only the exchange of information between neighboring nodes. The filter banks are therefore of low implementation complexity and suitable for processing large time-varying datasets. Numerical examples will demonstrate the effectiveness of the proposed designed methods. Application in time-varying graph signal denoising will show the superiority of joint time-vertex filter bank over other methods.

Wavelet-based multiresolution analysis coupled with deep learning to efficiently monitor cracks in concrete

Abstract: This paper proposes an efficient methodology to monitor the formation of cracks in concrete after non-destructive ultrasonic testing of a structure. The objective is to be able to automatically detect the initiation of cracks early enough, i.e. well before they are visible on the concrete surface, in order to implement adequate maintenance actions on civil engineering structures. The key element of this original approach is the wavelet-based multiresolution analysis of the ultrasonic signal received from a sample or a specimen of the studied material subjected to several types of solicitation. This analysis is finally coupled to an automatic identification scheme of the types of cracks based on artificial neural networks (ANNs), and in particular deep learning by convolutional neural networks (CNNs); a technology today at the cutting edge of machine learning, in particular for all applications of pattern recognition. Wavelet-based multiresolution analysis does not add any value in detecting fractures in concrete visible by optical inspection. However, the results of its implementation coupled with different CNN architectures show cracks in concrete can be identified at an early stage with a very high accuracy, i.e. around 98%, and a loss function of less than 0.1, regardless of the implemented learning architecture.

Real-Time Implementation of Multiband Spectrum Sensing Using SDR Technology.

Abstract: In this work, a novel multiband spectrum sensing technique is implemented in the context of cognitive radios. This technique is based on multiresolution analysis (wavelets), machine learning, and the Higuchi fractal dimension. The theoretical contribution was developed before by the authors; however, it has never been tested in a real-time scenario. Hence, in this work, it is proposed to link several affordable software-defined radios to sense a wide band of the radioelectric spectrum using this technique. Furthermore, in this real-time implementation, the following are proposed: (i) a module for the elimination of impulsive noise, with which the appearance of sudden changes in the signal is reduced through the detail coefficients of the multiresolution analysis, and (ii) the management of different devices through an application that updates the information of each secondary user every 100 ms. The performance of these linked devices was evaluated with encouraging results: 95% probability of success for signal-to-noise ratio (SNR) values greater than 0 dB and just five samples (mean) in error of the edge detection (start and end) for a primary user transmission.

Concrete Cracks Monitoring using Deep Learning-based Multiresolution Analysis

Abstract: In this paper, we propose a new methodology for crack monitoring in concrete structures. This approach is based on a n this paper, we propose a new methodology for monitoring cracks in concrete structures. This approach is based on a multi-resolution analysis of a sample or a specimen of the studied material subjected to several types of solicitation. The image obtained by ultrasonic investigation and processing by a dedicated wavelet will be analyzed according to several scales in order to detect internal cracks and crack initiation. The ultimate goal of this work is to propose an automatic crack type identification scheme based on convolutional neural networks (CNN). In this context, crack propagation can be monitored without access to the concrete surface and the goal is to detect cracks before they are visible on the concrete surface. The key idea allowing such a performance is the combination of two major data analysis tools which are wavelets and Deep Learning. This original procedure allows to reach a high accuracy close to 0.90. In this work, we have also implemented another approach for automatic detection of external cracks by deep learning from publicly available datasets.

Time-Domain Audio Source Separation With Neural Networks Based on Multiresolution Analysis

Abstract: We propose a time-domain audio source separation method based on multiresolution analysis, which we call multiresolution deep layered analysis (MRDLA). The MRDLA model is based on one of the state-of-the-art time-domain deep neural networks (DNNs), Wave-U-Net, which successively down-samples features and up-samples them to have the original time resolution. From the signal processing viewpoint, we found that the down-sampling (DS) layers of Wave-U-Net cause aliasing and may discard information useful for source separation because they are implemented with decimation. These two problems are due to the decimation; thus, to achieve a more reliable source separation method, we should design DS layers capable of simultaneously overcoming these problems. With this motivation, focusing on the fact that the successive DS architecture of Wave-U-Net resembles that of multiresolution analysis, we develop DS layers based on discrete wavelet transforms (DWTs), which we call the DWT layers, because the DWTs have anti-aliasing filters and the perfect reconstruction property. We further extend the DWT layers such that their wavelet basis functions can be trained together with the other DNN components while maintaining the perfect reconstruction property. Since a straightforward trainable extension of the DWT layers does not guarantee the existence of anti-aliasing filters, we derive constraints for this guarantee in addition to the perfect reconstruction property. Through music source separation experiments including subjective evaluations, we show the efficacy of the proposed methods and the importance of simultaneously considering both the anti-aliasing filters and the perfect reconstruction property.

Improved Convolutional Neural Multi-Resolution Wavelet Network for COVID-19 Pneumonia Classification

Abstract: Fast and early detection of infected patient is the most paramount step necessary to curb the spread of the COVID-19 disease. Radiographs have perhaps presented the fastest means of diagnosing COVID-19 in patients. The well-known standard for COVID-19 test requires a standard procedure and usually has low sensitivity. Previous studies have adopted various AI-based methods in detecting COVID-19 using both chest tomography and chest x-ray. In this study, the goal is to propose an enhanced convolutional neural multi-resolution wavelet network for COVID-19 pneumonia diagnosis. Our proposed model is a convolutional neural network integrated discrete wavelet transform of four level decomposition multiresolution analysis robust to handle few dataset which is very paramount due to the fast emergence of COVID-19. We evaluated our model based on three categories of public dataset of chest x-ray and chest tomography images. Our proposed model achieves 98.5% accuracy, 99.8% sensitivity, 98.2% specificity, and 99.6% AUC for multiple class categories with less training parameters. The results of this study show that our method achieves state-of-the-art result.

A Digital Heterodyne 2- To 150-kHz Measurement Method Based on Multiresolution Analysis

Abstract: A description is given of a new 2- to 150-kHz range frequency decomposition method, as required to support power grid compatibility level measurements. This real-time digital method is based on a tree structure of nominally identical modular algorithmic elements to provide a decomposition of the signal bandwidth resulting in a 200-Hz resolution. Each modular element divides the bandwidth of its input into a low-frequency and a high-frequency half. Elements connected in the tree result in a progressive increase in resolution at each level of the tree, hence multiresolution analysis. The modular element is based on heterodyning and down-sampling. Simplifications of the modular elements that result in an efficient process of changing the sign of alternate input samples, digital filtering, and discarding alternate samples at the output are presented. It is shown that these cloned modular elements form a computationally efficient algorithm that can operate in real-time. Refinements to cover gaps in the bandwidth which cause errors are explained. The algorithm is compatible with the traditional CISPR 16 analog heterodyne method. Test results are presented which show that the method achieves accuracies of ±5% of reading, as required for compatibility level measurements.

Wavelet geographically weighted regression for spectroscopic modelling of soil properties.

Abstract: Soil properties, such as organic carbon, pH and clay content, are critical indicators of ecosystem function. Visible-near infrared (vis-NIR) reflectance spectroscopy has been widely used to cost-efficiently estimate such soil properties. Multivariate modelling, such as partial least squares regression (PLSR), and machine learning are the most common methods for modelling soil properties with spectra. Often, such models do not account for the multiresolution information presented in the vis-NIR signal, or the spatial variation in the data. To address these potential shortcomings, we used wavelets to decompose the vis-NIR spectra of 226 soils from agricultural and forested regions in south-western Western Australia and developed a wavelet geographically weighted regression (WGWR) for estimating soil organic carbon content, clay content and pH. To evaluate the WGWR models, we compared them to linear models derived with multiresolution data from a wavelet decomposition (WLR) and PLSR without multiresolution information. Overall, validation of the WGWR models produced more accurate estimates of the soil properties than WLR and PLSR. Around 3.5-49.1% of the improvement in the estimates was due to the multiresolution analysis and 1.0-5.2% due to the integration of spatial information in the modelling. The WGWR improves the modelling of soil properties with spectra.

Wavelet regularization strategy for the fractional inverse diffusion problem

Abstract: This manuscript deals with an inverse fractional-diffusing problem, the time-fractional heat conduction equation, which is a physical model of a problem, where one needs to identify the temperature distribution of a semi-conductor, but one transient temperature data is unreachable to measurement. Mathematically, it is designed as a time-fractional diffusion problem in a semi-infinite region, with polluted data measured at x = 1, where the solution is wanted for 0 ≤ x < 1. In view of Hadamard, the problem extremely suffers from an intrinsic ill-posedness, i.e., the true solution of the problem is computationally impossible to measure since any measurement or numerical computation is polluted by inevitable errors. In order to capture the solution, a regularization scheme based on the Meyer wavelet is therefore applied to treat the underlying problem in the presence of polluted data. The regularized solution is restored by the Meyer wavelet projection on elements of the Meyer multiresolution analysis (MRA). Furthermore, the concepts of convergence rate and stability of the proposed scheme are investigated and some new order-optimal stable estimates of the so-called Holder-Logarithmic type are rigorously derived by carrying out both an a priori and a posteriori choice approaches in Sobolev scales. It turns out that both approaches yield the same convergence rate, except for some different constants. Finally, the computational performance of the proposed method effectively verifies the applicability and validity of our strategy. Meanwhile, the thrust of the present paper is compared with other sophisticated methods in the literature.

Multiresolution analysis for linear canonical S transform

Abstract: To deal with the time-varying signals, linear canonical S transform (LCST) is introduced to possess some desirable characteristics that are absent in conventional time–frequency transforms. Inspired by LCST, we in this paper developed an idea of novel MRA associated with LCST. Moreover, the construction method of orthogonal wavelets is developed. Finally an example is provided to justify the results.

Fractional multiresolution analysis and associated scaling functions in $$L^{2}({\mathbb {R}})$$ L 2 ( R )

Abstract: In this paper, we show how to construct an orthonormal basis from Riesz basis by assuming that the fractional translates of a single function in the core subspace of the fractional multiresolution analysis form a Riesz basis instead of an orthonormal basis In the definition of fractional multiresolution analysis, we show that the intersection triviality condition follows from the other conditions Furthermore, we show that the union density condition also follows under the assumption that the fractional Fourier transform of the scaling function is continuous at 0 At the culmination, we provide the complete characterization of the scaling functions associated with fractional multiresolution analysis

Spatial Multiresolution Analysis Approach to Identify Crash Hotspots and Estimate Crash Risk

Abstract: In this paper, we evaluate the performance of a spatial multiresolution analysis (SMA) method, that behaves like a variable bandwidth kernel density estimation (KDE) method, for hazardous r...

Effects of healthy aging on electrical activity of the brain during motor tasks characterized with wavelets

Abstract: Age-related changes in the brain’s electrical activity can be caused by healthy aging and brain disorders. The ability to detect such phenomena from an electroencephalogram (EEG) is important to identify diseases’ latent stages. These changes appear in the brain’s background electrical activity, but the performance of cognitive or motor tasks can cause more significant signs of impairments in brain dynamics. Here, we analyze the features of multichannel EEGs in groups of healthy elderly and younger adults during hand clenching and apply two wavelet-based methods to reveal distinctions that arise with age, namely multiresolution analysis using the discrete wavelet transform, and multifractal formalism, which involves extracting the skeleton of the continuous wavelet transform. With the first method, we demonstrate that inter-group differences are established at rest and during the performance of motor tasks. With the second method, we also find similar distinctions, although the number of suitable channels and their distribution can differ. We conclude that characterization of age-related differences depends on the wavelet-based method used for EEG processing.

Multidimensional fully adaptive lattice Boltzmann methods with error control based on multiresolution analysis

Abstract: Lattice-Boltzmann methods are known for their simplicity, efficiency and ease of parallelization, usually relying on uniform Cartesian meshes with a strong bond between spatial and temporal discretization. This fact complicates the crucial issue of reducing the computational cost and the memory impact by automatically coarsening the grid where a fine mesh is unnecessary, still ensuring the overall quality of the numerical solution through error control. This work provides a possible answer to this interesting question, by connecting, for the first time, the field of lattice-Boltzmann Methods (LBM) to the adaptive multiresolution (MR) approach based on wavelets. To this end, we employ a MR multi-scale transform to adapt the mesh as the solution evolves in time according to its local regularity. The collision phase is not affected due to its inherent local nature and because we do not modify the speed of the sound, contrarily to most of the LBM/Adaptive Mesh Refinement (AMR) strategies proposed in literature, thus preserving the original structure of any LBM scheme. Besides, an original use of the MR allows the scheme to resolve the proper physics by efficiently controlling the accuracy of the transport phase. We carefully test our method to conclude on its adaptability to a wide family of existing lattice Boltzmann schemes, treating both hyperbolic and parabolic systems of equation, thus being less problem-dependent than the AMR approaches, which have a hard time granting an effective control on the error. The ability of the method to yield a very efficient compression rate and thus a computational cost reduction for solutions involving localized structures with loss of regularity is also shown, while guaranteeing a precise control on the approximation error introduced by the spatial adaptation of the mesh. The numerical strategy is implemented on a specific open-source platform called SAMURAI with a dedicated data-structure relying on set algebra.

Wavelet Transform Based Fault Identification and Reconfiguration for a Reduced Switch Multilevel Inverter Fed Induction Motor Drive

Abstract: The multilevel inverter-based drive system is greatly affected by several faults occurring on switching elements. A faulty switch in the inverter can potentially lead to more losses, extensive downtime and reduced reliability. In this paper, a novel fault identification and reconfiguration process is proposed by using discrete wavelet transform and auxiliary switching cells. Here, the discrete wavelet transform exploits a multiresolution analysis with a feature extraction methodology for fault identification and subsequently for reconfiguration. For increasing the reliability, auxiliary switching cells are integrated to replace faulty cells in a proposed reduced-switch 5-level multilevel inverter topology. The novel reconfiguration scheme compensates open circuit and short circuit faults. The complexity of the proposed system is lower relative to existing methods. This proposed technique effectively identifies and classifies faults using the multiresolution analysis. Furthermore, the measured current and voltage values during fault reconfiguration are close to those under healthy conditions. The performance is verified using the MATLAB/Simulink platform and a hardware model.

A multiresolution adaptive wavelet method for nonlinear partial differential equations

Abstract: The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to solve partial differential equations (PDEs) with features evolving on a wide range of spatial and temporal scales. To meet these challenges, we present a multiresolution wavelet algorithm to solve PDEs with significant data compression and explicit error control. We discretize in space by projecting fields and spatial derivative operators onto wavelet basis functions. We provide error estimates for the wavelet representation of fields and their derivatives. Then, our estimates are used to construct a sparse multiresolution discretization which guarantees the prescribed accuracy. Additionally, we embed a predictor-corrector procedure within the temporal integration to dynamically adapt the computational grid and maintain the accuracy of the solution of the PDE as it evolves. We present examples to highlight the accuracy and adaptivity of our approach.

A Wavelet-Free Approach for Multiresolution-Based Grid Adaptation for Conservation Laws

Abstract: In recent years the concept of multiresolution-based adaptive discontinuous Galerkin (DG) schemes for hyperbolic conservation laws has been developed. The key idea is to perform a multiresolution analysis of the DG solution using multiwavelets defined on a hierarchy of nested grids. Typically this concept is applied to dyadic grid hierarchies where the explicit construction of the multiwavelets has to be performed only for one reference element. For non-uniform grid hierarchies multiwavelets have to be constructed for each element and, thus, becomes extremely expensive. To overcome this problem a multiresolution analysis is developed that avoids the explicit construction of multiwavelets.